Four particles are in a 2-D plane with masses, x- and y- positions, and x- and y

Question

Four particles are in a 2-D plane with masses, x- and y- positions, and x- and y- velocities as given in the table below:

m

x

y

vx

vy

  1  

7.7 kg

-2.5 m

-4.5 m

3.2 m/s

4.1 m/s

  2  

9.1 kg

-3.4 m

3.7 m

-5.1 m/s

5 m/s

  3  

8.5 kg

4.7 m

-5.6 m

-6 m/s

1.9 m/s

  4  

7.9 kg

5.6 m

2.5 m

-3.9 m/s

-3.2 m/s

1)

What is the distance the center of mass is from the origin?m

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2)

What is the x-component of the velocity of the center of mass?m/s

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3)

What is the y-component of the velocity of the center of mass?

m

x

y

vx

vy

  1  

7.7 kg

-2.5 m

-4.5 m

3.2 m/s

4.1 m/s

  2  

9.1 kg

-3.4 m

3.7 m

-5.1 m/s

5 m/s

  3  

8.5 kg

4.7 m

-5.6 m

-6 m/s

1.9 m/s

  4  

7.9 kg

5.6 m

2.5 m

-3.9 m/s

-3.2 m/s

Explanation / Answer

X component of ceter of mass =m1x1+m2x2+m3x3+m4x4/m1+m2+m3+m4

=7.7×-2.5+9.1×-3.4+8.5×4.7+7.9×5.6/7.7+9.1+8.5+7.9=1.024m

Y component =

7.7×-4.5+9.1×3.7-8.5×5.6+7.9×2.5/7.7+9.1+8.5+7.9=-0.8684m

X component of velocity  

7.7×3 .2+9.1×-5.1+8.5×-6+7.9×-3.9/7.7+9.1+8.5+7.9

=-3.1198m

Y component of velocity

7.7×4.1+9.1×5+8.5×1.9+7.9×-3.2/7.7+9.1+8.5+7.9=2.04638m

7

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